Coot Bird Behavior-Based Optimization Algorithm For Optimal Placement Of Thyristor Controlled Series Compensator Devices In Transmission Power Networks

POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Coo Bi d Beha io -Based Op imiza ion Algo i hm Fo Op imal Placemen O Thy is o Con olled Se ies Compensa o De ices In T ansmission Powe Ne wo ks Anh Tuan NGUYEN1, Chi Kien LE2, Minh Tan PHAN3T ung Thang NGUYEN3 1Ph.D. S uden , Facul y o Elec ical and Elec onics Enginee ing, Ho Chi Minh Ci y Uni e si y o Technology and Educa ion, 01 Vo Van Ngan s ee , Thu Duc Dis ic , 700000, Ho Chi Minh ci y, Vie nam 2Facul y o Elec ical and Elec onics Enginee ing, Ho Chi Minh Ci y Uni e si y o Technology and Educa ion, 01 Vo Van Ngan s ee , Thu Duc Dis ic , 700000, Ho Chi Minh ci y, Vie nam 3Powe Sys em Op imiza ion Resea ch G oup, Facul y o Elec ical and Elec onics Enginee ing, Ton Duc Thang Uni e si y, 19 Nguyen Huu Tho s ee , Tan Phong wa d, Dis ic 7, 700000 Ho Chi Minh Ci y, Vie nam uanna.ncs@hcmu e.edu. n, kienlc@hcmu e.edu. n, phanminh[email p o ec ed], nguyen[email p o ec ed] DOI: 10.15598/aeee. 21i3.5244 A icle his o y: Recei ed May 25, 2023; Re ised Jul 25, 2023; Accep ed Aug 21, 2023; Published Sep 30, 2023. This is an open access a icle unde he BY-CC license. Abs ac . This s udy p esen s he new applica ion o Coo bi d beha io -based op imiza ion algo i hm (COOTBA) o op imal placemen o Thy is o Con- olled Se ies Compensa o (TCSC) de ices in an IEEE 30-node ansmission powe ne wo k wi h h ee single objec i es, including uel cos , powe loss, and ol age de ia ion. COOTBA is implemen ed o he sys em wi h one case wi hou TCSC de ices and h ee o he s wi h TCSC. COOTBA can each smalle cos and loss han p e ious algo i hms by om 0.04% o 3.78%, and om 6.7% o 40.3% in he i s case wi h- ou TCSC. In he second case wi h TCSC, COOTBA can each smalle cos han o he s by om 0.008% o 0.66%. In addi ion, he compa isons o esul s om COOTBA in he h ee cases wi h TCSC indica e ha TCSC should be op imized o bo h loca ion and eac- ance, and he limi a ion o TCSC de ices should be high enough. Thus, COOTBA is an e ec i e algo i hm o op imizing TCSC de ices on ansmission powe sys ems. Keywo ds Coo bi ds, Thy is o con olled se ies compen- sa o , ansmission powe ne wo k, uel cos , powe loss, ol age de ia ion. 1. In oduc ion. P oblem De ini ion A powe sys em’s mos basic elec ic pa s a e powe plan s, ansmission g ids, dis ibu ion g ids, and loads [1]. Typically, he wo p ima y componen s o powe plan s a e gene a o s and ans o me s, whe eas ans- mission g ids and dis ibu ion g ids a e mainly com- p ised o lines, ans o me s, buses, and loads. T ans- mission and dis ibu ion g ids ha e almos he same elec ic componen s bu di e en sizes. G ea e com- ponen size is o ansmission g ids, bu a smalle size is o dis ibu ion g ids. Gene a o s and ans o me s a powe plan s a e in cha ge o p oducing and ans- mi ing elec ici y o ansmission lines [2]. Dis ibu- ion lines ecei e elec ici y om ansmission lines and p o ide elec ici y o loads. T ansmission lines play a e y impo an ole in powe sys ems since hey ecei e a e y high powe om powe plan s and supply he powe o dis ibu ion powe ne wo ks. I he ans- mission lines canno wo k s ably, powe gene a ed by powe plan s canno be p o ided o dis ibu ion lines and loads [3]. So, op imal powe low (OPF) o ans- mission powe ne wo ks has become a signi ican p ob- lem in powe sys ems. The con en ional OPF p oblem has a ac ed a as numbe o s udies o eaching di e en objec i e unc- c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 171 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Tab. 1: Nomencla u e NT Gs Numbe o he mal gene a o s in exis ing powe sys em α1n,α2n,α3nFuel coe icien s o he mal gene a o n P Gn,QGnAc i e and eac i e powe gene a ed by he he mal gene a o n CDab Conduc ance o he ansmission line a−b Uaand UbVol age ampli udes a node aand node b NND Numbe o nodes o he gi en ansmission ne wo k P Gls n,P Ghs nThe lowes and highes ac i e powe gene a ion o he n h he mal gene a o QGls n,QGhs nThe lowes and highes eac i e powe gene a ion o he n h he mal gene a o SCls a,SChs aThe lowes and he highes eac i e powe gene a ion o he shun capaci o s a node a Uls load,Uhs load The lowes and he highes ol age magni udes o load a he load node d Uls n,Uhs nThe lowes and he highes ol age magni udes o he he mal gene a o n NNLS Numbe o load nodes T Sls ,T Shs The lowes and he highes ap se ing alue o all ans o me s T SpTap se ing alue o he ans o me p N ms T ans o me numbe APkAppa en powe ansmi ed h ough he b anch k AP hs kThe highes appa en powe o he b anch k NB s B anch numbe Xls T CSC ,Xhs T CSC The lowes and highes eac ance alues o TCSC de ices XT CSC,q The eac ance o he TCSC q NT CSC The numbe o TCSC B T CSC,q The b anch wi h he q h TCSC dn0÷1A andom numbe wi hin one and ze o ions such as elec ic gene a ion uel cos educ ion [4] and pollu ed emission educ ion [5] o he mal powe plan s (ThPPs), and ol age p o ile enhancemen [6]. When he end o using enewable ene gies becomes popula , wind and sola pho o ol aic powe plan s a e conside ed wi h ThPPs as majo powe sou ces in ansmission powe ne wo ks [7]. Howe e , a big p ob- lem o ansmission powe ne wo ks is he con ingency o ansmission lines once powe plan s upg ade hei powe o loads need mo e powe [8]. The addi ional in- s alla ion o he mal gene a ing uni s, he ins alla ion o new wind powe plan s and new sola pho o ol aic powe plan s, he addi ional ins alla ion o wind u - bines o sola pho o ol aic a ays in exis ing enewable powe plan s, o changes in mode n echnologies a e he eason ha ansmission lines cope wi h he s a us o o e cu en [9]. The key mo i e o OPF is o ind he op imal ope a- ion plan o gene a ing uni s and o he elec ic de ices o cu ing he elec ic p oduc ion cos and ene gy loss and enhancing powe quali y such as equency, ol - age, and high eliabili y while sa is ying all cons ain s om hese componen s [10]. In simula ing he OPF p oblem, hanks o he aid o so wa e, pa ame e s o elec ic componen s a e modeled as con ol a iables and dependen a iables in which con ol a iables and dependen a iables a e, espec i ely, ega ded as in- pu da a and esul s o he New on-G aphson me hod [11]. I he wo ypes o a iables a e wi hin allowable limi s, he e is a alid solu ion o powe low. How- e e , an op imal solu ion mus sa is y all cons ain s and ha e a good objec i e unc ion [12]. Conside ing he se ious issue o con ingency, inding solu ions o he OPF p oblem ake mo e challenges, o e en he e a e no alid solu ions ound by e y s ong me hods o he cases. Combining powe low me hods such as Gaussidel/New on-G aphson and he me aheu is ic algo i hms is he mos e ec i e end [13]-[15]. Ma h- powe was un o calcula ing powe lows; meanwhile, an imp o ed gene ic algo i hm [13], imp o ed cuckoo sea ch [14], and Jelly ish sea ch algo i hm (JSA) [15] we e success ully applied o inding con ol a iables. Howe e , i powe plan s mus p oduce high powe and ansmi o loads, hese e y high-pe o mance me h- ods also ail o ind easonable solu ions. De i ed om he unexpec ed issues, Flexible Al e - na ing Cu en T ansmission Sys em (FACTSs) com- ponen s ha e been sugges ed o be used in powe sys- ems. Se e al FACTS de ices ha e been applied o minimize ac i e powe loss, educe ol age d op, and a oid con ingency, such as S a ic Va Compensa o (SVC) [16], s a ic synch onous compensa o (STAT- COM) [17], Thy is o Con olled Se ies Compensa o (TCSC) [1], [18]-[24], Uni ied Powe Flow Con olle (UPFC) [25, 26], Thy is o Con olled Phase-Angle Regula o (TCPAR) [25], he combina ion o TCPAR and TCSC [27]-[30], and he combina ion o SVC and TCSC [31]. Se e al s udies ha e conside ed he same FACTs, bu di e en me aheu is ic algo i hms we e used. The s udy [1] was a e y ea ly s udy abou TCSC by p oposing a hyb id Simula ed annealing al- go i hm and Tabu sea ch algo i hm (SAA/TSA) in 2002. The s udy has also implemen ed Gene ic algo- i hm (GA), Tabu sea ch algo i hm (TSA), and Simu- la ed annealing algo i hm (SAA) o in es iga ing he solu ions ob ained by SAA/TSA. The s udy [16] has sol ed a mul iobjec i e unc ion, and i has used A mul iobjec i e biogeog aphy-based op imiza ion algo- c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 172 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER i hm (MOBBO). The s udy [17] also op imized he ins alla ion o STATCOM and UPFC o educe cu - en on ansmission lines. Pa icle swa m op imiza- ion (PSO) [18], imp o ed an lion algo i hm (IALA) [19], and Gene ic algo i hm (GA) [20, 21] we e e- spec i ely applied o op imizing TCSC in ansmis- sion powe ne wo ks. Two imp o ed e sions o pa - icle swa m op imiza ion we e espec i ely applied in he s udies [22, 23], including Cons ic ion ac o -based pa icle swa m op imiza ion algo i hm (CF-PSO) [22], and challenge s and aging leade algo i hm-based pa - icle swa m op imiza ion (CALA-PSO) [23]. CF-PSO was a popula imp o ed e sion o PSO ha has been applied o many op imiza ion p oblems in enginee - ing. Meanwhile, CALA-PSO was i s de eloped in he s udy [23]. The s udy [24] has de eloped a hy- b id ha mony sea ch algo i hm and di e en ial e olu- ion algo i hm (HAS/DE) o he OPF p oblem wi h TCSC; howe e , he s udy has no implemen ed single algo i hms, such as ha mony sea ch algo i hm and Di - e en ial e olu ion o he same p oblem in he s udy [24]. The s udy [25] has sugges ed using an imp o ed g asshoppe algo i hm (IGRA) o op imize he ins al- la ion o ei he UPFC o TCPAR in he ansmission powe ne wo k. Di e en algo i hms, such as hyb id PSO [27], k ill he d algo i hm (KHA) [28], symbio ic o ganisms sea ch algo i hm (SOSA) [29], and nondomi- na ed so ing gene ic algo i hm-II (NSGA-II) [30], ha e been applied o op imizing TCPAR and TCSC simul- aneously. The s udies ha e indica ed ha he numbe o FACTs de ices had a clea impac on he imp o e- men o he ol age o loads, ene gy loss educ ion, and educ ion o elec ic gene a ion cos s. GA, di e en ial e olu ion (DE), and pa icle swa m op imiza ion ha e been applied o op imizing bo h SVC and TCSC. SVC could compensa e o eac i e powe a nodes ins alled wi h SVC; meanwhile, TCSC could educe a pa o a pa ame e o ansmission lines. So, he h ee al- go i hms ha e imp o ed he echnical indica o s o he applied sys ems, bu hei e ec i eness was di - e en . In gene al, hese s udies ha e applied di e en FACTs in ansmission powe sys ems o echnical and economic ac o s. The esul s we e much be e han hose o base ansmission powe sys ems wi hou he FACTs de ice. In his s udy, we apply an e ec i e me aheu is ic algo i hm, Coo bi d beha iou -based op imiza ion al- go i hm (COOTBA) o he OPF p oblem wi h he placemen o TCSC de ices in a ansmission powe ne wo k wi h 30 nodes. COOTBA has been p o en o be e y e ec i e o placing sola gene a o s in dis ibu- ion sys ems [31, 32]. The s udy [33] applied COOTBA o an op imal powe low conside ing load nodes wi h aluminum plan s o educing emission and powe loss. COOTBA was p o ed o be success ul o he p oblem and o be mo e e ec i e han glowwo m swa m algo- i hm (GWSA) o all s udy cases. The pe o mance o COOTBA was p o ed o be high o op imiza ion p oblems in ansmission and dis ibu ion ne wo ks, al- hough i has no been shown o be be e han all ex- is ing me hods. So, COOTBA is applied in he s udy o he OPF p oblem wi h he p esence o TCSC. The no el y o he s udy is as ollows: •Find he maximum limi o TCSC o he high- es cos and loss educ ions, and he bes ol age imp o emen . •Compa e he pe o mance o COOTBA and p e i- ous algo i hm in [34] in inding op imal loca ions o TCSC. The con ibu ion o he s udy a e as ollows: •Reach smalle elec ici y gene a ion cos s, smalle powe losses and be e ol age p o ile han p e i- ous s udies. •Find he mos op imal solu ions o TCSC in e- ducing elec ici y gene a ion cos and powe loss, and imp o ing ol age. •Find a sui able algo i hm, COOTBA, o he placemen o TCSC in ansmission powe ne - wo ks. 2. P oblem desc ip ion 2.1. Objec i e unc ions This s udy conside s h ee objec i e unc ions (OFs) while e alua ing he con ibu ions o TCSC in ans- mission powe ne wo ks, including o al uel cos min- imiza ion (TFC) [35], ac i e powe loss minimiza ion (APL) [36], and ol age de ia ion minimiza ion (VD) [12]. Thei ma hema ical exp essions a e, espec i ely, p esen ed as ollows: TFC = NT Gs X n=1 α1n+α2n.PGn+α3n.PG2 n(6S/h),(1) APL = NND X a=1 NND X b=1,b6=a CDab.(U2 a+U2 b −2.Ua.Ub.cos φab)(MW),(2) V D = NND X a |Ua−UST R|(Pu).(3) In Equa ion (2), ϕab is ob ained by using ϕab =ϕa− ϕbwhe e ϕaand ϕba e ol age phase angels a node aand node 4. In Equa ion (3), UST R is he s anda d ol age alue, and i s alue is se o a a ed alue o 1.0 pu. c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 173 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Fig. 1: A simple illus a ion o he TCSC ins alled in he spe- ci ic ansmission line. 2.2. The desc ip ion o TCSC Thy is o con olled se ies compensa o (TCSC) is one o he FACTs de ices ha can be ins alled in ansmis- sion powe ne wo ks o economic and echnical a - ge s such as powe gene a ion, ol age d op educ ion, powe loss educ ion, e c. In a ansmission line wi h he p esence o TCSC, he line model is plo ed in Fig- u e 1 [37]. The eac ance model o he line a e ins alling TCSC is ob ained by: X0 ab =Xab −XT CSC .(4) In addi ion, he ans e conduc ance and he suscep- ance o he line a−ba e ins alling a TCSC de ice a e ecalcula ed by [38]: CDT CSC ab =Rab R2 ab + (Xab −XT CSC )2,(5) STT CSC ab =−(Xab −XT CSC ) R2 ab + (Xab −XT CSC )2,(6) whe e CDT CSC ab and STT CSC ab a e, espec i ely, he conduc ance and he suscep ance o he line a−ba e he TCSC de ice is placed on he line; Raband Xaba e, espec i ely, he esis ance and eac ance o he ans- mission line a−bbe o e ins alling TCSC; XT CSC is he eac ance o he TSCS de ice placed on he ans- mission line a−b. No e ha CDT CSC ab =CDT CSC ba and STT CSC ab =STT CSC ba a e used as conside ing he ac o s in ansmission powe ne wo ks. 2.3. Cons ain s o OPF p oblem wi h TCSC 1) Equali y cons ain In OPF p oblem, he ac i e and eac i e powe balance cons ain s a each node a(whe e a= 1, . . . , NND) mus be sa is ied as shown in he ollowing exp essions [39]: PGa−PDa=Ua NNo X b=1 Ub"CDT CSC ab .cos(φab) +STT CSC ab .sin(φab)#,(7) QGa+SCa−QDa=Ua NNo X b=1 Ub"CDT CSC ab .cos(φab) −STT CSC ab .sin(φab)#, (8) whe e PGaand QGba e, espec i ely, he ac i e and eac i e powe injec ed a node aby he mal gene a- o s; PDaand QDba e, espec i ely, he ac i e and eac i e powe demands o loads a node a; and SCa is he eac i e powe supplied by he eac i e powe compensa o s connec ed a node a. 2) Inequali y cons ain s These cons ain s a e conside ed o sa is y ope a ion limi s o elec ic componen s in he ansmission powe ne wo ks, such as he mal gene a o s, shun capaci o s, loads, ans o me s, ansmission b anches, and addi- ionally added TCSC de ices. The cons ain s a e ex- p essed as ollows [1],[37],[40]: PGls n⩽PGn⩽PGhs n,(9) QGls n⩽QGn⩽QGhs n,(10) SCls a⩽SCa⩽SChs a;a= 1, ..., NND,(11) Uls load ⩽Uload ⩽Uhs load;load = 1, ..., NNLs,(12) Uls n⩽Un⩽Uhs n;n= 1, ..., NT Gs,(13) TSls p⩽TSp⩽TShs p;p= 1, ..., NT ms,(14) APk⩽APhs k;k= 1, ..., NB s,(15) Xls T CSC ⩽XT CSC,q ⩽Xhs T CSC ;q= 1,2, .., NT CSC , (16) 1⩽B T CSC,q ⩽NB s;q= 1,2, ..., NT CSC .(17) 3. Coo bi d beha iou -based op imiza ion algo i hm (COOTBA) COOTBA is also a me aheu is ic algo i hm based on popula ion and andomiza ion. COOTBA is a ma he- ma ical model exp essing he beha io s o an a e age- size wa e bi d species, Coo s, while sea ching o ood. Coo s end o ga he in a g oup wi h many indi idu- als, and hey mo e o ind ood oge he . Based on he amoun o ood ound, all coo s a e classi ied in o a membe g oup and a leade g oup. COOTBA has a di e en cons uc ion om o he me aheu is ic al- go i hms due o he special cha ac e is ic o he coo bi d species. COOTBA also needs a andomly ini ial solu ion se , and hen he solu ion se can be imp o ed based on wo echniques. The ini ial solu ion se and i s upda e p ocess a e p oduced and implemen ed as ollows: The ini ial solu ion se has an uppe bound and a lowe bound, Boundup and Boundlow, in which he bounds con ain he maximum and minimum alues o con ol a iables in a conside ed op imiza ion p ob- lem, espec i ely. Each solu ion is ep esen ed o a c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 174 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER coo in he swa m, and i is modeled by Coo c(whe e c= 1, . . . , SP o, and SP o is he alue o popula ion). Each Coo cis p oduced wi hin he ange [Boundlow, Boundup]. Each solu ion is exp essed by MCoo ain a low-quali y se and LCoo bin a high-quali y se . The e a e Nlow and Nhigh solu ions in he wo se s, espec- i ely. COOTBA upda es new solu ions o he wo se s as ollows: 3.1. Upda ing solu ions o he low-quali y se In he low-quali y solu ion se , COOTBA conside s h ee condi ions o upda e cu en solu ions acco d- ingly. The cu en and new solu ions a e se o MCoo aand MCoo new a, espec i ely. One ou o he ollowing equa ions is applied o p oduce he new so- lu ions. MCoo new a=MCoo a+SF1.(Coo d −MCoo a), (18) MCoo new a=SF2.(MCoo a+MCoo a0,)(19) MCoo new a=LCoo d +SF3.(LCoo d −MCoo a), (20) Whe e SF1,SF2, and SF3a e scaling ac o s gi en in Appendix A; MCoo a0is he closes solu ion o MCoo a;MCoo d is a newly gene a ed solu ion wi hin he ange [Boundlow,Boundup]; and LCoo d is a andom solu ion in he high-quali y se . 3.2. Upda ing solu ions o he high-quali y solu ion se COOTBA uses wo o mulas o sea ch new solu ions in he solu ion space, ei he Equa ion (21) o Equa ion (22). In he equa ions, LCoo band LCoo new ba e he b h cu en and new solu ions in he popula ion. To selec one ou o he wo equa ions, a andom numbe wi hin ze o and one is p oduced and compa ed o 0.5. I he numbe is smalle han 0.5, Equa ion (21) is applied. O he wise, Equa ion (22) is selec ed. The wo equa ions a e as ollows: LCoo new b=Coo bes +SF4(Coo bes −LCoo b) (21) LCoo new b=−Coo bes +SF4(Coo bes −LCoo b) (22) whe e Coo bes is he bes solu ion in he high-quali y se ; and SF4is a scaling ac o gi en in Appendix A. 3.3. Applica ion o COOTBA o OPF p oblem wi h TCSC In his s udy, COOTBA is esponsible o inding con- ol pa ame e s o he con en ional OPF p oblem and TCSCs’ pa ame e s. Sec ion 2 has men ioned hese pa ame e s. The con en ional OPF p oblem’s pa am- e e s mus sa is y cons ain s (9), (11), (13) and (14) meanwhile TCSCs’ pa ame e s mus sa is y cons ain s (16) and (17). A e ha ing hese pa ame e s, Ma h- powe p og am is un o eaching dependen pa ame- e s o he OPF p oblem, which can sa is y cons ain s (10), (12) and (15). I hese dependen pa ame e s a e no allen in o he limi s, hey mus be ined o ind- ing penal y e ms. Finally, objec i e unc ions in Eqs. (1)-(3) can be ob ained. The lowcha o applying COOTBA o he p oblem is p esen ed in Figu e 2. 4. Nume ical esul s In he sec ion, COOTBA is implemen ed o he IEEE 30-node ansmission powe sys em o op imizing he placemen o TCSC de ices wi h h ee di e en single objec i e unc ions, including cos , ac i e powe loss, and ol age de ia ion. In addi ion, COOTBA is also implemen ed o he base sys em wi hou TCSC o he same objec i es. The sys em is plo ed in Figu e 2, and i s da a can be aken om [41]. The limi a- ions o eac ance o TCSC a e om 0.0 o 0.02 pu [1]. Fo he case o using a sui able loca ion o TCSC wi hou using he sea ch om COOTBA, he sole lo- ca ion ob ained by implemen ing he loss sensi i i y index me hod [34] is inhe i ed o be b anch 3-4. The h ee s udy cases a e exp essed in de ail as ollows: •Case 1: COOTBA is implemen ed o he sys em wi hou TCSC de ices. Fo his case, SP o and MI e a e, espec i ely, se o 20 and 200 by ex- pe imen •Case 2: Line 3-4 is employed o placing TCSC. COOTBA is implemen ed o inding pa ame e s in he powe sys em and eac ance o TCSC. Fo his case, SP o and MI e a e, espec i ely, se o 40 and 200 by expe imen . •Case 3: COOTBA is implemen ed o inding pa- ame e s in he powe sys em, and loca ion and eac ance o TCSC. Fo his case, SP o and MI e a e, espec i ely, se o 40 and 500 by expe imen . •Case 4: Simila o Case 3, bu he maximum limi o TCSC is one pu ins ead o 0.02 pu as in Case 3. The se ings o SP o and MI e a e simila o hose o Case 3. c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 175 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Fig. 2: Applica ion o COOTBA o OPF p oblem wi h TCSC de ices. Fig. 3: The IEEE 30-node sys em. To each objec i es in he ou cases abo e, COOTBA is implemen ed o 50 ial uns. Ma lab so wa e wi h e sion 2018b is used o code he p o- g am, and a pe sonal compu e wi h he p ocesso o 2.4 GHz and 8 GB o RAM is p o ided o ins alling he Ma lab so wa e. 4.1. Resul compa ison o 3 cases Table 2 p esen s he bes uel cos , he bes powe loss, and he bes ol age de ia ion o he h ee cases abo e om 50 success ul uns o each case. In gene al, Case 3, wi h op imal loca ion and pa ame e o TCSC, is he bes o op imizing he conside ed objec i es, cos , loss, and ol age. The base sys em wi hou TCSC in Case 1 is he wo s case o educing uel cos and im- p o ing ol age, bu Case 2 is he wo s o educing powe loss. In de ail, he h ee alues a e espec i ely $799.378, 2.946 MW and 0.142 Pu in Case 1, $799.314, 2.954 MW and 0.140 pu in Case 2, and $799.207, 2.929 MW, and 0.138 pu in Case 3. A s ange issue is ha Case 2 wi h TCSC a he p ede e mined line 3-4 su - e s a highe powe loss han he base sys em o Case 1 by (2.954-2.946=0.008 MW). This unexpec ed esul indica es ha he placemen o TCSC on ansmission line 3-4 is ine ec i e in educing powe loss. Case 3 inds he ansmission line 2-5 o TCSC, and his so- lu ion is mo e e ec i e han Case 2 by eaching a loss educ ion o (2.954-2.929=0.025 MW). Taking a look a he eac ance o TCSC can see ha Case 2 needs a 0.0176-pu, 1.52e-06-pu, and 0.0067-pu TCSC bu Case 3 needs he maximum eac ance o 0.02 pu o all h ee s udy cases. Case 2 wi h powe loss ob- jec i e needs app oxima ely ze o eac ance o TCSC c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 176 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Tab. 2: Summa y o he bes esul s om h ee s udy cases by unning COOTBA S udy Resul Objeci e unc ion Case Fuel cos ($) Powe loss (MW) Vol age de ia ion (pu) Case 1 Objec i e alue 799.378 2.946 0.142 Case 2 Objec i e alue 799.314 2.954 0.140 XT CSC (Pu) 0.0176 1.52e-06 0.0067 Case 3 Objec i e alue 799.207 2.929 0.138 XT CSC (Pu) 0.02 0.02 0.02 Loca ion o TCSC Line 2-5 Line 2-5 Line 1-18 wi h he alue o 1.52e-06 pu. The op imal ansmis- sion line o placing a TCSC de ice is line 2-5 o cos and loss objec i es and line 18-1 o he ol age ob- jec i e. I is no ed ha i he TCSC de ice wi h a highe maximum limi o 0.02 Pu, he e ec i eness o he TCSC de ice is g ea e han Case 3. In ac , Case 4 is implemen ed, and i s esul s a e p esen ed in Table 3. I can be seen clea ly ha he cos , loss, and ol age de ia ion o Case 4 a e be e han hose o Case 3 in Table 2 by $0.08, 0.033 MW, and 0.026 pu. Case 4 uses he same line 2-5 as Case 3 o cos op imiza ion bu di e en lines o loss and ol age de ia ion objec- i es. Line 27-28 and line 10-20 a e employed by Case 4 ins ead o line 2-5 and line 1-18 o loss and ol - age de ia ion. The eac ance o TCSC is also di e en be ween Case 3 and Case 4. The eac ance alues o Case 4 a e, espec i ely, 0.0497, 0.2620, and 0.3998 pu, while hose o Case 3 a e 0.02. Tab. 3: Summa y o he bes esul s om Case 4 by unning COOTBA Resul Objeci e unc ion Cos ($) Loss (MW) Vol. De . (pu) Objec i e alue 799.127 2.896 0.116 XTCSC (Pu) 0.0497 0.2620 0.3998 Loca ion o TCSC Line 2-5 Line 27-28 Line 10-20 The uel cos o gene a o s is plo ed in Figu e 4 and Figu e 5 o compa e Case 2 and Case 1, and Case 3 and Case 1. The wo igu es show ha he same gen- e a o s ha e a e y small cos di e ence. In addi ion, he sa ing cos o each gene a o in Case 2 and Case 3 is also calcula ed as compa ed o Case 1 and plo ed by using blue a eas in he wo igu es. Gene a o s 1 and 5 o Case 2 and Case 3 use smalle cos han hose o Case 1 by $0.65 and $2.03, and $0.68 and $0.95 bu o he gene a o s 2, 3 and 4 o Case 2 and Case 3 use highe cos han hose o Case 1. Gene a o 6 o Case Fig. 4: Compa ison o gene a o uel cos be ween Case 2 and Case 1. Fig. 5: Compa ison o gene a o uel cos be ween Case 3 and Case 1. 2 and Case 3 ha e he same cos as Case 1. The esul s indica e ha he placemen o TCSC on ansmission line 3-4 in Case 2 and ansmission line 2-5 in Case 3 changed he powe gene a ed by gene a o s and led o cos educ ion. The con e gence p ocesses o each he bes cos o Cases 1 and 2, and Cases 3 and 4 a e gi en in Figu e 6 and Figu e 7. The igu es show ha COOTBA always each be e cos in Case 2 han Case 1, and in Case 4 han Case 3 a he same i e a ion. A he inal i e - a ion, he cos s o Case 2 and Case 4 a e espec i ely be e han hose o Case 1 and Case 3. The ol age o 30 nodes o he ol age de ia ion objec i e is plo ed in Figu e 8 o compa ing Case 2 and Case 1, and in Figu e 9 o compa ing Case 3 and Case 1. The wo igu es indica e ha he powe sys em in he h ee s udy cases can sa is y ol age cons ain s. Nodes ha e a ange o ol age om highe han 0.97 pu and smalle han 1.04 pu, in which he limi s o ol age a e om 0.95 o 1.05 pu. The ol age di e ence a nodes is no clea be ween Case 2 and Case 1, and c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 177 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Fig. 6: Con e gence p ocesses o each he bes cos o Cases 1 and 2. Fig. 7: Con e gence p ocesses o each he bes cos o Cases 1 and 2. Case 3 and Case 1. Clea ly, COOTBA is e y use ul in op imizing he con ol pa ame e s o he base sys em in Case 1. So, he use o TCSC in Case 3 canno each much be e esul s han in Case 1. To cla i y he e ec i eness o COOTBA, he ollowing sec ion will compa e he pe o mance o COOTBA wi h p e ious me hods o s udy cases. 4.2. Compa ison o pe o mance be ween COOTBA and o he s COOTBA is compa ed o o he me hods o Case 1 wi hou TCSC o cos and loss objec i es in Table 4. COOTBA is compa ed o adap i e PSO (APSO) [42], cons ic ion ac o -based PSO (CF-PSO) [43], imp o ed CF-PSO (ICF-PSO) [43], imp o ed g oup sea ch op imiza ion algo i hm (IGSOA) [44], con en- ional Honey Bee Ma ing algo i hm (CHBMA) and imp o ed o CHBMA (IHBMA) [45], mul i-objec i e ma hema ical p og amming algo i hm (MOMPA) [46], Fig. 8: Vol age o nodes in Case 1 and Case 2. Gaussian ba e bone impe ialis compe i i e op imiza- ion algo i hm (GBBICOA), modi ied social spide al- go i hm (MSSA) [48], imp o ed e olu ion p og am- ming algo i hm (IEPA) [49], eaching and lea ning based algo i hm (TLBA) [50] and hyb id TLBA, and impe ialis compe i i e algo i hm (HTLBA-ICA) [50]. The cos compa ison shows ha COOTBA is supe io o many algo i hms o cos objec i e and loss objec- i es, excluding ICF-PSO [43] and MSSA [48]. Fo he cos compa ison, COOTBA has ound a smalle cos han o he s, om $0.292 (compa ed o CF-PSO[43]) o $31.472 (compa ed o GBBICOA [47]), co espond- ing o 0.04% o 3.78%. Fo loss compa ison, COOTBA has ound a smalle loss han o he s, om 0.21 MW o 1.991 MW, co esponding o om 6.7% o 40.3%. How- e e , COOTBA is wo se han MSSA and ICF-PSO due o a highe cos o $0.038. So, COOTBA is also a highly e ec i e algo i hm, and i s esul s om TCSC de ice placemen a e highly eliable. Tab. 4: Compa ison o cos and powe loss om Case 1 Me hod SAA/TSA [1] APSO [42] Cos ($) 804.7837 801.97 Me hod GBBICOA [47] MSSA [48] Cos ($) 830.85 799.34 Me hod IGSOA [44] CHBMA [45] Cos ($) 801.75 802.21 Me hod HTLBA-ICA [50] CF-PSO [22] Cos ($) 801.0488 799.9512 Me hod CF-PSO [43] ICF-PSO [43] Cos ($) 799.67 799.34 Me hod IEPA [49] TLBA [50] Cos ($) 802.465 801.6524 Me hod IHBMA [45] MOMPA [46] Cos ($) 801.99 801.76 Me hod HAS/DE [24] COOTBA Cos ($) 799.5762 799.378 Me hod MOMPA [46] GBBICOA [47] Powe loss (MW) 3.156 4.937 Me hod MSSA [48] COOTBA Powe loss (MW) 2.945 2.946 c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 178 POWER ENGINEERING AND ELECTRICAL ENGINEERING VOLUME: 21 |NUMBER: 3 |2023 |SEPTEMBER Fig. 9: Vol age o nodes in Case 1 and Case 3. As conside ing he OPF p oblem wi h TCSC, he uel cos s a e compa ed in Table 5. Abou he uel cos o Case 2, COOTBA has eached a smalle cos han all compa ed algo i hms, including SAA/TSA [1], CF-PSO [22], HAS/DE [24] by $5.335, $0.460, $0.060, co esponding 0.66%, 0.058%, and 0.008%. Clea ly, COOTBA is a high-pe o mance algo i hm o he OPF p oblem wi h he placemen o TCSC de ices. Howe e , when applying he no el y wi h he de e - mina ion o op imal loca ions (Case 3) and inc ease o TCSC limi , which is highe han 0.02 Pu (Case 4), COOTBA could each much smalle cos s han hese me hods. COOTBA s ill used he uppe limi wi h 0.02 Pu o TCSC in Case 3, bu i used a highe alue o TCSC wi h 0.0497 Pu in Case 4. And he change o assump ions (loca ion o placing TCSC and TCSC limi ) has led o a clea e ec i eness in educing elec- ici y gene a ion cos . Tab. 5: Compa ison o cos and powe loss om Case 1 Me hod Fuel cos ($) XT CSC (pu) SAA/TSA [1] (Case 2) 804.6497 0.02 CF-PSO [22] (Case 2) 799.7741 0.0107 HAS/DE [24] (Case 2) 799.3743 0.0200 COOTBA (Case 2) 799.314 0.0176 COOTBA (Case 3) 799.207 0.02 COOTBA (Case 4) 799.127 0.0497 5. Conclusion This s udy applied Coo bi d beha io -based op imiza- ion algo i hm o sol ing op imal powe lows o he IEEE 30-node ansmission powe ne wo k. Fou s udy cases ha e been implemen ed, in which Case 1 neglec s, bu o he s conside TCSC de ices. Case 2 only op i- mized he eac ance o TCSC, while Case 3 and Case 4 op imized bo h loca ion and eac ance o TCSC. Case 3 used he maximum eac ance o 0.02 pu; meanwhile, Case 4 expanded he ange o 1.0 Pu. The esul s can be summa ized as ollows: •COOTBA was supe io o abou i y o he algo- i hms in p e ious s udies o Case 1. As com- pa ed o he wo s compa ed algo i hm, COOTBA could each a smalle cos and loss by 3.78% and 40.3%, espec i ely. •COOTBA could each less cos han h ee al- go i hms, including a hyb id me aheu is ic algo- i hm and imp o ed e sions o PSO o Case 2. The highes educ ion in cos could be up o 0.66%. •Case 3 could each smalle cos , loss, and ol age de ia ion han Case 1 and Case 2, bu i eached wo se alues han Case 4. The esul s indica ed ha COOTBA is e y e ec i e o he con en ional OPF p oblem and expanded OPF p oblem wi h TCSC de ices. COOTBA was e ec i e in sea ching he loca ion and eac ance o TCSC de- ices. Ano he algo i hm based on loss sensi i i y ac- o s was applied o ind ansmission line 3-4 o TCSC placemen , bu COOTBA could ind mo e sui able ansmission lines. Wi h di e en limi s o TCSC’s e- ac ance, COOTBA ound di e en lines, and he di e - en lines could lead o be e esul s han o he s ud- ies. So, he s udy has high con ibu ions o applying COOTBA and sugges s op imizing bo h eac ance and loca ion o TCSC. Howe e , he s udy has unexpec ed sho comings in e ms o he pe o mance o COOTBA and he conside a ion o mo e se ious cons ain s. In he u u e, he s udy will be imp o ed by conside ing mo e FACTs de ices such as SVC, UPFC, and TCPAR o imp o ing he e ec i eness o ansmission powe ne wo ks wi h la ge-scale up o 118 nodes. On he o he hand, enewable ene gies will be employed, and he FACTS de ices will be employed o a oid he o e - load s a us o lines as well as imp o e uel cos , powe loss, and ol age p o ile o ansmission powe sys ems. Au ho Con ibu ions Bo h N.A.T. and T.M.P. pe o med he analy ic cal- cula ions and pe o med he nume ical simula ions. L.C.K. and T.T.N w o e he whole pape . N.A.T. and T.T.N con ibu ed o he inal e sion o he manusc ip . Re e ences [1] ONGSAKUL, W. and P. BHASAPUTRA. Op i- mal powe low wi h FACTS de ices by hyb id c 2023 ADVANCES IN ELECTRICAL AND ELECTRONIC ENGINEERING 179